Dispersion theoretic calculation of the $H\to Z+\gamma$ amplitude

Abstract

We have calculated the $W$-loop contribution to the amplitude of the decay $H\to Z+\gamma$ in two different methods: 1) in the $R_{\xi }$-gauge using dimensional regularization (DimReg), and 2) in the unitary gauge through the dispersion method. Using the dispersion method we have followed two approaches: i) without subtraction and ii) with subtraction, the subtraction constant being determined adopting the Goldstone boson equivalence theorem (GBET) at the limit $M_W\to 0$. The results of the calculations in $R_{\xi }$-gauge with DimReg and the dispersion method with the GBET completely coincide, which shows that DimReg is compatible with the dispersion method obeying the GBET.

Comments: 16 pages with 15 figures, changes in Sec. IVB, references added